§1. On the emergence of informationistic worldview (informatism)
When looking at the development of European thought from bird’s-eye view, we observe three great periods of mutual influences between the state of science (that is, empirical teories with mathematics) and a dominant philosophical worldview: the theistic (or theological) period of the Middle Ages, mechanicistic from the Renaissance dawn of modernity, and informationistic as dawning in our times. If we liked to most briefly define each period with one key concept, we could mark them up, respectively, with the key categories: God, hardware, software.
Dependencies between these two intellectual forces are always mutual though in various proportions; even in the Middle Ages when theology dominated so strongly, it was influenced e.g. by mathematics in the Pythagorean and Platonian spirit as well as encouraged mathematicians to bold speculations about infinity (which ancient mathematicians were afraid of). Impressive examples of the impact of natural theology (of Platonian brand) on optics and astronomy are found in Kepler who in this respect continued some medieval threads (Grosseteste’s metaphysics of light, etc).
A next nice example of such a feedback is found at the Renaissance eve of modern science. Scientists were then massively influenced by the mechanicist worldview of the ancient atomists. In turn, as a result of successes due to that inspiration, the mechanicist model of the universe has got firmly rooted in science, and in circles of educated public, till our times.
Nowadays the time is rape for replacing the mechanicist model of the world by what deserves to be called informationistic worldview. Before defining this phrase, I suggest that we also accept its handy terminological equivalent to be used interchangeably. Let it be the term informatism which has gained a noticeable place in the literature. When using the latter for the sake of convenience, we shall remember that the full meaning is involved in the original version which has been introduced after the following consideration.
The English language offers quite a number of adjective derivatives from the noun “information”. Thus we have: informational, informatist, informationist, informatic, informatistic, informationistic, informatized. Some of them seem to be synonymous, some not. This a real “embarass de richesse”. Fortunately, a convicing hint as to the choice comes from an article in the journal “Information, Communication & Society” (Volume 2, Issue 1, 1999) by Jos de Mul. Its title reads: The Informatization of the Worldview, and inside there appears the key term informationistic worldview. Its author is Professor of Philosophical Anthropology at the Erasmus University in Rotterdam. Prof. de Mul depicts the mechanistic approach as descending from the historical scene at which there emerges the informationistic worldview as characteristic of the coming time.
This is also the point of the Polish study which appeared in Spring 2011 (with Academic Publishing House “Exit” in Warsaw) under the title: “Umysł – Komputer – Świat. O zagadce umysłu z informatycznego punktu widzenia”. Part One written by Paweł Stacewicz is entitled -“Infomatyczna inżynieria umysłu”, Part Two, by Witold Marciszewski – “Światopogląd ery informatycznej“. The term italicized is one to be rendered with “informationistic”, and so the above phrases get translated as follows. The book title: Mind – Computer- World. On the riddle of mind from an informationistic point of view. The Part One: Informationistic engineering of mind; the Part Two: The worldview of the informationistic era. Moreover, the term “informatism” (Polish “informatyzm”) is frequently employed throughout the book.
Chapter 16 of this book presents the ancient atomism as a paradigm of extreme mechanicism, focussed, so to speak, entirely on a hardware, with negligence of the role of software in natural and social processes. Moreover, in agreement with Mul’s point, it is acknowledged that mechanicism inspired modern science in its beginnings and several next centuries. However, in the last decades the concept of information processing, conceived as computing, provides a paradigmatic model for natural and social sciences.
Informatism emerges from several sources: (i) logical research in the foundations of mathematics and computation, (ii) merging of computation theory with physics (iii) computer technology, (iv) biological reaearch as in genetics and neurobiology, (v) some speculative conjectures about computational nature of the universe, inspired by the earlier listed points.
What is remarkable about this worldview, it is the fact that nobody does pretend to be its author. It is rather a content of spontateous social awarensess shaped by the participation in the society massively saturated with digital technology and informationistic vernacular. This state of affairs forms a challenge for philosophers, in particular those concerned with philosophy of science and epistemology. Informatism is an epistemological position when cognition is conceived as problem-oriented information processing, and the latter as a kind of computing — the main concern of informatics.
Informatism can be presented in one of two ways. One of them would take advantage of the fact that there exist valuable partial approches which might be merged into a desirable synthesis. However, this ought to be a huge research project to be executed by a team of first-class specialists in the fields of complexity, computability, quanta, cosmology (universe as a computer), etc. The more difficult would be such a task that among the views to be considered some opposite other ones; then we would be bound to precisely analyze their arguments before trying a synthesis. As a material to such processing one should take into accont, for instance, Ed Fredkin’s digital philosophy, John Wheeler’s idea about “it from bit”, likewise opposing their “digitalism” Freeman Dyson who vigorously defends the necessity of analog (i.e. non-digital) computing.
§2. From insight to algorithm, and the other way round
To define a worldview one should refer to its main tenets, especially its key concepts and central questions. The key concepts of informationistic worldview (italicized below) are grouped around the pair: algorithm versus insight (i.e. intuition). Algorithm is a way of mechanical information-processing, or computing, aimed to solve a certain problem. As insight also has an essential share in problem-solving, hence there arises the central issue of the informationistic worldview: how insight and algorithm relate to each other?
Once upon the time, the concept of insight was not much esteemed by those so-called analytic philosophers who saw its place rather in the sphere of poetry, metaphysics, religion, etc. However, the situation is different at the start of the 21-st century. Let me exemplify this fact by a personal remembering.
Several years ago a friend of mine acted as the editor of a volume on automated theorem proving. Since he knew about my interest in the subject, he asked for a suggestion as to the title of the planned volume. I suggested “From Insight to Proof” — meaning formalized, that is, algorithmized proofs alone; for only such proofs are what proof-automation theorists are aiming at. Thus the suggested phrase might have been generalized as “from insight to algorithm” (obviously, in that project the more specific title version was preferred). I was happy to see that my advice has been willingly accepted by the editor and all the contributors (who belonged to the best specialists in the field). The more happy I was when the volume appeared, and I found in it two contributions regarding a Gödelian approach to the “insight vs proof” issue which is in the centre of my interests. Such an experience would be incogitable in the heyday of Vienna Circle, that is, before Gödel’s discovery of arithmetical sentences which intuitively prove true, but their truth cannot be demonstrated in an algorithmic way.
To fully express the main tenet of informationistic worldview, the said phrase should be completed as follows: from insight to algorithm, and the other way round: from algorithm to insight. This is the case of a positive feedback being, nicely illustrated with the success of arithmetic. There must have been a very penetrative mathematical insight (of an anonymous Hindu more than thousand years ago) that resulted in the discovery that there exists the number zero to precede one (the idea alien to Greek and Roman mathematicians). This made it possible for the Arab scholar Al-Chwarismi to create algorithms for addition etc. This relieved mathematicians from the enormous losses of time and energy (as those caused by old Roman notation), opening new chances before their creative thought which, in turn, could have produced new algorithms.
Such mutual support of insight and algorithm belongs to the main forces in the dynamics of human knowledge. In order to perceive other forces, and have a look at the whole dynamics (as seen by informationistic worldview), a certain conceptual confusion should be removed. The concept guilty of this confusion is that of computing (see the listing of key notions above) and its derivative computability. In the idiom of computer scientists “to compute” means: to process information exactly according to an algorithm. That is: to mechanically follow its instructions. These tell us: (1) how to transform physical shapes of formulas, (2) doing this step by step, without any leaps of intuition, (3) up to obtaining solution of the problem in question (4) in a finite number of steps.
The above procedure can be performed by a human calculator using pencil and a sheet of paper, or by a computing machine as defined mathematically by Alan Turing in 1936, and for this reason called Turing machine. Now its physical realization is present everywhere as electronic digital computer. The range of possibilities and the mode of proceding of digital computers is exactly what people call camputing in an everyday idiom.
However, such a narrow notion of computing induces the crisis of conceptual confusion. While in the main stream resarch people stick to the equivalence of the terms “computing” and “algorithmic digital computing”, there is a fairly large group of dissidents who back their claim as follows. The main stream definition is inconsistent, since in the accepted at large vabulary of computer science we have the term “analog computing”; it is what is being done by analog devices, and nobody refuses to call them computers. Hence we are bound either (i) to accept contradiction that analog devices are computers and are no computers (as not acting algorithmically and digitally), or (ii) to more broadly define the notion of computing so that it embrace both algorithmic and non-algoritmic information processing as two varieties of computing.
§3. Insights in analog computing and in perceiving abstract entities
From among the two strategies stated above, we are bound to follow the latter, if we do not like committing contradiction. This, in turn, implies the duty to explain how broadly should we understand analog computing. Surely this concept is satisfied by what is done by analog computers. These do not operate with symbolic representations (as digit sequences) of, say, physical quantities. Instead, (1) they process quantities of a certain kind (eg. electric) which represent quantities of another kind (eg. mechanical), and (2) such quantities may be continuous. Now, what about the phenomenon of insights?
With the computing being performed by analog devices some insights share the lack of symbolization and the mapping of some quantities into other quantities. This is satsfied, for instance, in the case of car driver whose problem-solving consists of a sequence of decisions. His inference do not need any representations by linguistic units. He reasons with visual representations which are mappings of what happens on the road. Also the feature of continuity can be satified in mapping: it is shared by a section of road and its mental picture. The same can be said about a shooter trying to hit a target; he acts in a continuous external environment which he maps in his inside.
The things appear less obvious in a case like that of a preacher who feels, and so reproduces in himself, the mood of his audience and adapts his performance to such a feeling. Moods and atttitudes are not physical quantities. However, the instance may be interpreted as follows. The preacher’s insight consists in an empathic sharing of his audience’s mood, hence a kind of mapping. This information is by him processed to compute possibly best reactions to listeners’ attitudes towards his teaching.
Thus both types of cases, that of car driver and that of preacher, may be subsumed under the category of analog computing as information in them processed is not symbolic. It consists of pictures of an external reality which are somehow mapped in the reasoner’s “inside” (i.e. his mind? brain?). His reasoning operates not with linguistic units but with mapped pictures. In driver’s case these are spatial images of continuous quantities as distance, velocity etc. In preacher’s case occur less tangible images of audience’s mental and emotional states, but nevertheless they are mapped, and the reasoning preserves the feature of operating on such non-symbolic mappings.
It may seem that insights, as being instantaneous, have nothing to do with computing as being a sequence of steps. Hower, when we combine an introspective perception of our insights with what we know from neurobiological research, then there comes the following understanding: the experience of insight results from a sequence of events occurring in the nervous system. The last element, being an insight, is one whose we are aware, while the preceding ones (a nervous process of analog computing) are hidden before the “eye” of consciousness. Thus insights enter into a harmony with analog computing.
What about perceiving abstract entities, as sets, functions, numbers, and in particular infinite numbers? Infinite magnitudes in no way can be derived by abstraction from sense experiences. Hence propositions about infinities rank as the most spectacular truths of reason.
In this context, it is in order to clarify that the informationistic worldview does not expect any infallibility, or absolute reliability, from human reason. Similarily, the sound empiricism does not claim that all sense perceptions are unconditionally true. The name “truth of reason” hints at reason as the sorce of the given statement, and at truth as the goal endeavoured. A mathematical theorem which has been disproved as well as mathematical theorems which has been duly demonstrated are at the same footing as propositions born from reason, and not from another source, say, senses or taste. Therefore, the term judgement of reason should be recommended instead of that old Leibnizian phrase, but the latter may be used for historical associations, provided that no confusion would arise.
One may speculate that there exist abstract entities which are mapped in minds in a process of mathematical cognition. However, we are not bound to risk such conjectures. Should they prove true, then we shall state that such insights are analog in their nature; but if not, then we shall treat them as a separate category. What really matters. it the fact that not all truths are attainable in an algoritmic way.